The Linear Complexity of q-ary Generalized Cyclotomic Sequences of Period p~m
Xiaoni Du · Journal of Wuhan University · 2013
Assume that p is a prime and q is a positive integer with q|(p-1).Families of q-ary generalized cyclotomic sequences of period pm are introduced by defining eneralized cyclotomic classes over Zpm and extended constructions of certain binary generalized cyclotomic sequences in the literature.The linear complexities of such sequences are determined when q is an odd prime or q=4,respectively.The results indicate that the linear complexities are larger than a half of the period and such sequences can resist attacks by the Berlekamp-Massey algorithm.At the same time,a construction of p-ary generalized cyclotomic sequences of period pm is presented using the similar way and its linear complexity is conjectured.